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This paper provides an algebraic formalization of mathematical structures formed by fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom has been given by G. Schmidt and T. Str ohlein. Unlike Boolean relation algebras, fuzzy relation algebras are not… (More)

This paper provides a notion of Zadeh categories as a categorical structure formed by fuzzy relations with sup-min composition, and proves two representation theorems for Dedekind categories (relation categories) with a unit object analogous to one-point set, and for Zadeh categories without unit objects.

- Rudolf Berghammer, Bernhard Möller, Georg Struth, Jules Desharnais, Gunther Schmidt, April +12 others
- 2008

Preface This volume contains the tutorial materials and the contributed extended ab-The programme has been organised for the second time in association with RelMiCS/AKA. It took place in Frauenwörth on an Island in Lake Chiem in Bavaria, from April 7 to April 11, 2008, and included invited tutorials, a student session and attendance at the conference. Eight… (More)

- Hitoshi Furusawa, I Acknowledgements
- 1998

The aim of this thesis is to develop the fuzzy relational calculus. To develop this calculus, we study four algebraic formalisations of fuzzy relations which are called fuzzy relation algebras, Zadeh categories, relation algebras and Dedekind categories, and we strive to arrive at their representation theorems. The calculus of relations has been… (More)

- Hitoshi Furusawa
- 1996

This paper provides an algebraic characterization of mathematical structures formed by cartesian products of fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom was given by G. Schmidt and T. Str ohlein, and cartesian products of Boolean relation algebras… (More)

We reconstruct Peleg’s concurrent dynamic logic in the context of modal Kleene algebras. We explore the algebraic structure of its multirelational semantics and develop an axiomatization of concurrent dynamic algebras from that basis. In this context, sequential composition is not associative. It interacts with parallel composition through a weak… (More)